{"paper":{"title":"Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Leonardo Castellani, Paolo Aschieri","submitted_at":"1997-05-27T18:33:39Z","abstract_excerpt":"We review the construction of the multiparametric quantum group $ISO_{q,r}(N)$ as a projection from $SO_{q,r}(N+2) $ and show that it is a bicovariant bimodule over $SO_{q,r}(N)$. The universal enveloping algebra $U_{q,r}(iso(N))$, characterized as the Hopf algebra of regular functionals on $ISO_{q,r}(N)$, is found as a Hopf subalgebra of $U_{q,r}(so(N+2))$ and is shown to be a bicovariant bimodule over $U_{q,r}(so(N))$. An R-matrix formulation of $U_{q,r}(iso(N))$ is given and we prove the pairing $U_{q,r}(iso(N))\\leftrightarrow ISO_{q,r}(N)$. We analyze the subspaces of $U_{q,r}(iso(N))$ tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9705023","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}